Two dimensional materials include materials where one dimension is at the atomic scale. Such materials include but are not limited to graphene, molybdenum disulfide (MoS2), titanium disulfide (TiS2) and other like materials. These two dimensional materials have been demonstrated to possess excellent mechanical and electrical properties which make them useful nano-scale sensors, including for pressure sensing. For example, Graphene has a Young's modulus of one terapascal (1 TPa) and has been demonstrated to be impermeable to gases, such as described in Lee, C., et al., Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene, Science, 2008, 321(5887), p. 385-388, and Bunch, J. S., et al., Impermeable atomic membranes from graphene sheets, Nano Letters, 2008, 8(8): p. 2458-2462. Graphene has further been demonstrated to be a zero-band gap semiconductor with useful transconductive properties, such as described in Dean, C. R., et al., Boron nitride substrates for high-quality graphene electronics, Nature Nanotechnology, 2010, 5(10): p. 722-726, and Petrone, N., et al., Chemical Vapor Deposition-Derived Graphene with Electrical Performance of Exfoliated Graphene, Nano Letters, 2012, 12(6): p. 2751-2756. Such properties may be used to fabricate a two dimensional material-based pressure sensor.
Graphene is a single atomic layer of carbon atoms closely packed in a honeycomb lattice, such as described in Geim, A. K. and K. S. Novoselov, The rise of graphene, Nature Materials, 2007, 6(3): p. 183-191. Further, graphene possesses unique mechanical and electrical properties that makes it well suited for nano-scale sensors. Graphene is the strongest known material with a Young's modulus of one terapascal (1 TPa) and the ability to withstand strains on the order of twenty percent (20%), such as described in Lee, C., et al., Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene, Science, 2008, 321(5887), p. 385-388. Moreover, as a true two-dimensional material, it has virtually no bending stiffness and, thus, acts as an ideal membrane, such as described in Lee, C., et al., Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene, Science, 2008, 321(5887), p. 385-388, and Freund, L. B. and S. Suresh, Thin film materials: stress, defect formation, and surface evolution, 1st pbk. ed 2009, Cambridge, England; N.Y.: Cambridge University Press, xviii, p. 750. Further, graphene membranes have been shown to be impermeable to gases and may withstand large pressures prior to breaking, delamination, or slipping, as described in Bunch, J. S., et al., Impermeable atomic membranes from graphene sheets, Nano Letters, 2008, 8(8): p. 2458-2462, and Bunch, J. S. and M. L. Dunn, Adhesion mechanics of graphene membranes, Solid State Communications, 2012, 152(15): p. 1359-1364. These properties combine to make graphene an appropriate material for pressure sensing applications, such as described in Bunch, J. S., et al., Impermeable atomic membranes from graphene sheets, Nano Letters, 2008, 8(8): p. 2458-2462, and Koenig, S. P., et al., Ultrastrong adhesion of graphene membranes, Nature Nanotechnology, 2011, 6(9): p. 543-546, and Bunch, J. S. and M. L. Dunn, Adhesion mechanics of graphene membranes, Solid State Communications, 2012, 152(15): p. 1359-1364.
While the unique mechanical properties of graphene may enable the ability to fabricate diaphragm-based pressure sensors which may withstand large, pressure-induced mechanical deflections, the ability to sense these changes may not be achieved through a piezoresistive effect common to most pressure transducers. Graphene may not exhibit a significant piezoresistive effect with applied strain, as shown with both Raman spectroscopy and in-situ nanoindentation measurements, as described in Huang, M., et al., Electronic—Mechanical Coupling in Graphene from in situ Nanoindentation Experiments and Multiscale Atomistic Simulations, Nano Letters, 2011, 11(3): p. 1241-1246, and Huang, M., et al., Phonon softening and crystallographic orientation of strained graphene studied by Raman spectroscopy, Proceedings of the National Academy of Sciences of the United States of America, 2009, 106(18): p. 7304-7308. These experiments report a gauge factor of one and nine-tenths (1.9) for graphene, which is equivalent to that of a metal foil strain gauge, as described in Huang, M., et al., Electronic—Mechanical Coupling in Graphene from in situ Nanoindentation Experiments and Multiscale Atomistic Simulations, Nano Letters, 2011, 11(3): p. 1241-1246, and Barlian, A. A., et al., Review: Semiconductor Piezoresistance for Microsystems, Proceedings of the IEEE, 97(3): p. 513-552. A low gauge factor may be expected as graphene is a zero bandgap semiconductor with a symmetric lattice and, as it is bi-axially strained at relatively low levels, there should only be a resistance change based upon a change in geometry, which is the same mechanism in a metallic strain gauge. Alternatively, a semiconductor strain gauge made of silicon, for example, will exhibit piezoresistive gauge factors on the order of two hundred (200) due to the fact that there is a significant change in silicon's mobility with strain, as described in Barlian, A. A., et al., Review: Semiconductor Piezoresistance for Microsystems, Proceedings of the IEEE, 97(3): p. 513-552.
While graphene may not possess a high gauge factor, it does exhibit significant changes in conductivity with an applied electric field. Changes in the applied electric field may increase or decrease the carrier concentration in graphene, which may directly change the resistance of the graphene, as described in Tan, Y.-W., et al., Measurement of scattering rate and minimum conductivity in graphene, Physical Review Letters, 2007, 99(24): p. -. One of the advantages of transconductance-based sensing is the potential for substantially higher sensitivities, as the change in resistance of a device with an applied electric field has been observed to be more than one thousand percent (1,000%), as described in Petrone, N., et al., Chemical Vapor Deposition-Derived Graphene with Electrical Performance of Exfoliated Graphene, Nano Letters, 2012, 12(6): p. 2751-2756. Conventional sensing methods such as piezoresistance may typically exhibit changes in resistance on the order of two percent (2%) to ten percent (10%) and may be material limited to relatively low strain levels of less than one percent (1%), as described in Barlian, A. A., et al., Review: Semiconductor Piezoresistance for Microsystems, Proceedings of the IEEE, 97(3): p. 513-552.
Transduction methods of measuring pressure may include a piezoelectric method, an optical method, and a capacitive method. Pressure transducers are typically large with diaphragm sizes on the order of about five hundred microns (500 μm) to five millimeters (5 mm), as described in Barlian, A. A., et al., Review: Semiconductor Piezoresistance for Microsystems, Proceedings of the IEEE, 97(3): p. 513-552, and Senturia, S. D., Microsystem design 2001, Boston: Kluwer Academic Publishers, xxvi, p. 689, and Baxter, L. K. and IEEE Industrial Electronics Society, Capacitive sensors: design and applications, IEEE Press series on electronics technologyl 997, New York: IEEE Press. xiv, p. 302. Such diaphragm dimensions may be needed to achieve sufficient electrical signals from pressure changes. Further, such diaphragm dimensions may be constrained by material properties and fabrication. For example, silicon may not be consistently micro-machined as an unsupported, pressure sensitive diaphragm to a single atomic layer. These limitations may result in a limit to the spatial resolution of pressure that may be measured. They further limit the frequency response of the transducer, as pressure transducer, no matter what method of transduction, respond as second-order under-damped, spring-mass-damper systems with typical resonant frequencies from about one kilo-Hertz (1 kHz) to about one mega-Hertz (1 MHz). It should be recognized that frequencies of greater than about one mega-Hertz (1 MHz) may only be achieved for high-pressure piezoresistive and optical-based pressure transducers. The frequency response of diaphragms may be typically taken to be about twenty percent (20%) of the natural frequency of the device, as described in Ogata, K., Modern control engineering, 4th ed. 2002, Upper Saddle River, N.J.: Prentice Hall, xi, p. 964. The resonance frequency of the diaphragm may decrease with increasing diaphragm size, which may result in reducing the useable frequency response range of the diaphragm.